# Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space

arXiv: https://arxiv.org/abs/1602.06522 · HTML: https://mlsanity.com/paper/1602.06522/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2016.

## Built on by (most cited first, 21 of 21)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [Multi-modal Entity Alignment in Hyperbolic Space](https://mlsanity.com/paper/2106.03619/) (2021)
- [WGCN: Graph Convolutional Networks with Weighted Structural Features](https://mlsanity.com/paper/2104.14060/) (2021)
- [Small Transformers Compute Universal Metric Embeddings](https://mlsanity.com/paper/2209.06788/) (2022)
- [The AI Revolution: Opportunities and Challenges for the Finance Sector](https://mlsanity.com/paper/2308.16538/) (2023)
- [L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classification](https://mlsanity.com/paper/2403.06064/) (2024)
- [Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networks](https://mlsanity.com/paper/2405.15481/) (2024)
- [A group-theoretic framework for machine learning in hyperbolic spaces](https://mlsanity.com/paper/2501.06934/) (2025)
- [How Low Can You Go? Searching for the Intrinsic Dimensionality of Complex Networks using Metric Node Embeddings](https://mlsanity.com/paper/2503.01723/) (2025)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [Adaptive Latent Space Tuning for Non-Stationary Distributions](https://mlsanity.com/paper/2105.03584/) (2021)
- [Strain-Minimizing Hyperbolic Network Embeddings with Landmarks](https://mlsanity.com/paper/2207.06775/) (2022)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Trivial bundle embeddings for learning graph representations](https://mlsanity.com/paper/2112.02531/) (2021)
- [Exploiting the geometry of heterogeneous networks: A case study of the Indian stock market](https://mlsanity.com/paper/2404.04710/) (2024)
- [MiranDa: Mimicking the Learning Processes of Human Doctors to Achieve Causal Inference for Medication Recommendation](https://mlsanity.com/paper/2408.01445/) (2024)
- [Network Alignment](https://mlsanity.com/paper/2504.11367/) (2025)
- [Hyperbolic Graph Embeddings: a Survey and an Evaluation on Anomaly Detection](https://mlsanity.com/paper/2512.18826/) (2025)
- [Train Small, Deploy Large: Zero-Shot GNN Transfer Through Geometric Renormalization](https://mlsanity.com/paper/2607.27767/) (2026)
- [Hyperbolic Graph Embedders for Link Prediction and Topology Reconstruction](https://mlsanity.com/paper/2608.07029/) (2026)

## Abstract (arXiv)

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity Similarity Optimization (PSO) model represents - at the moment - the climax of this theory. It suggests that the trade-off between node popularity and similarity is a mechanism to explain how complex network topologies emerge - as discrete samples - from the continuous world of hyperbolic geometry. The hyperbolic space seems appropriate to represent real complex networks. In fact, it preserves many of their fundamental topological properties, and can be exploited for real applications such as, among others, link prediction and community detection. Here, we observe for the first time that a topological-based machine learning class of algorithms - for nonlinear unsupervised dimensionality reduction - can directly approximate the network's node angular coordinates of the hyperbolic model into a two-dimensional space, according to a similar topological organization that we named angular coalescence. On the basis of this phenomenon, we propose a new class of algorithms that offers fast and accurate coalescent embedding of networks in the hyperbolic space even for graphs with thousands of nodes.